Question

The produce market is having a sale on grapes and oranges. A customer found the following two receipts in her cart as she was walking into the store. Use the information from the receipts to write a system of linear equations that can be used to determine the price per pound of grapes and the price per pound of oranges. Then, use the system to test the following solutions to determine which solution is viable. A. Given these constraints, grapes cost $3.25 per pound, and oranges cost $1.05 per pound. B. Given these constraints, grapes cost $1.60 per pound, and oranges cost $2.15 per pound. C. Given these constraints, grapes cost $1.05 per pound, and oranges cost $3.25 per pound. D. Give these constraints, grapes cost $2.15 per pound, and oranges cost $1.60 per pound.

Answer 1

Answer:

D

Step-by-step explanation

Let x be the cost of 1 lb of grapes and y be the cost of 1 lb of oranges

Then,

2x + 4y = $ 10.70

3x + 2y= $9.65

The value of an equation doesn't change if we multiply both L.H.S and R.H.S by the same number.

3(2x + 4y) = 3 * $10.70

6x + 12y = $32.10 .............(1)

2( 3x + 2y) = 2 * $ 9.65

6x + 4y = $19.30 ..........(2)

Using elimination method,        (1) - (2),

6x + 12y - (6x + 4y) = $32.10 - $19.30

6x + 12y -6x  -4y = $ 12.80

8y = $12.80

y = ($12.80)/8

Therefore, y = $1.60

The cost of 1 lb of oranges = y = $1.60

2x + 4y = $ 10.70

2x + 4 * $1.60 = $ 10.70

2x + $6.40 = $10.70

2x = $10.70 - $6.40

2x = $4.30

x = $2.15

The cost of 1 lb of grapes = x = $ 2.15

Hope it helps : )

Any doubts?